PSAT Math : Pattern Behaviors in Exponents

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : How To Find Patterns In Exponents

Solve for

\left ( \frac{2}{3} \right )^{x+1} = \frac{27}{8}

Possible Answers:

None of the above

Correct answer:

Explanation:

\left ( \frac{2}{3} \right )^{x+1} = \frac{27}{8} = \left ( \frac{3}{2} \right )^{3} = \left ( \frac{2}{3} \right )^{-3}

  which means

Example Question #253 : Exponents

Which of the following statements is the same as:

Possible Answers:

Correct answer:

Explanation:

Remember the laws of exponents. In particular, when the base is nonzero:

An effective way to compare these statements, is to convert them all into exponents with base 2. The original statement becomes:

This is identical to statement I. Now consider statement II:

Therefore, statement II is not identical to the original statement. Finally, consider statement III:

which is also identical to the original statement. As a result, only I and III are the same as the original statement. 

Example Question #3 : How To Find Patterns In Exponents

Write in exponential form:

Possible Answers:

Correct answer:

Explanation:

Using properties of radicals e.g.,

we get

Example Question #4 : How To Find Patterns In Exponents

Write in exponential form:

Possible Answers:

Correct answer:

Explanation:

Properties of Radicals

Example Question #11 : Pattern Behaviors In Exponents

Write in radical notation:

Possible Answers:

Correct answer:

Explanation:

Properties of Radicals

Example Question #261 : Exponents

Express in radical form :

Possible Answers:

Correct answer:

Explanation:

Properties of Radicals

Example Question #263 : Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

 

Example Question #11 : How To Find Patterns In Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

Convert the given expression into a single radical e.g. the expression inside the radical is:

 

and the cube root of this is :

Example Question #261 : Exponents

Solve for .

Possible Answers:

Correct answer:

Explanation:

 

Hence  must be equal to 2.

Example Question #581 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Now

Hence the correct answer is

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